Given a summand a n , we seek the “indefinite sum” S ( n ) determined (within an additive constant) by [Formula: see text] or, equivalently, by [Formula: see text] An algorithm is exhibited which, given a n , finds those S ( n ) with the property [Formula: see text] With this algorithm, we can determine, for example, the three identities [Formula: see text] [Formula: see text] and [Formula: see text] and we can also conclude that [Formula: see text] is inexpressible as S ( m ) - S (0), for any S ( n ) satisfying Eq. 2.
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R. William Gosper (1978) studied this question.